On the Well Posed Problems for a Class of PDE with Double Characteristics

Abstract:

      In^[1]、[2], F. Treves and G.Y.Wang at. al. have studied the following equation L_pu≡u_xx-x²u_ii pu_i=0, where p stands for a real parameter; They proved that both the Cauchy problem and Goursat problem have a unique solution if and only if p = 2h l. where h≥0 is an integer.